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Field of higher mathematics
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are
Geometric_analysis
Multiscale geometric analysis or geometric multiscale analysis is an emerging area of high-dimensional signal processing and data analysis. Wavelet Scale
Multiscale_geometric_analysis
Academic journal
Geometric and Functional Analysis (GAFA) is a mathematical journal published by Birkhäuser, an independent division of Springer-Verlag. The journal is
Geometric and Functional Analysis
Geometric_and_Functional_Analysis
Field of geometry and statistics
Geometric data analysis comprises geometric aspects of image analysis, pattern analysis, and shape analysis, and the approach of multivariate statistics
Geometric_data_analysis
Branch of mathematics
geometry is also related to the geometric aspects of the theory of differential equations, otherwise known as geometric analysis. Differential geometry finds
Differential_geometry
Branch of mathematics
from mathematical analysis, and introducing the Riemann surface, and Henri Poincaré, the founder of algebraic topology and the geometric theory of dynamical
Geometry
Branch of mathematics
Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in
Mathematical_analysis
Method of digital signal processing
Geometric phase analysis is a method of digital signal processing used to determine crystallographic quantities such as d-spacing or strain from high-resolution
Geometric_phase_analysis
American mathematician
include differential geometry and partial differential equations, with geometric analysis in particular. His most notable work includes the discovery of the
Peter_Li_(mathematician)
American mathematician (born 1942)
1942) is an American mathematician and one of the founders of modern geometric analysis. She is a professor emerita of mathematics at the University of Texas
Karen_Uhlenbeck
A rigid body with 3 distinct axes of inertia is unstable rotating about the middle axis
inertia with respect to a fixed axis of rotation Poinsot's ellipsoid – Geometric method for visualizing a rotating rigid body Polhode – Curve produced
Tennis_racket_theorem
Russian mathematician (born 1966)
is known for his contributions to the fields of geometric analysis, Riemannian geometry, and geometric topology. In 2005, Perelman resigned from his research
Grigori_Perelman
American mathematician (1943–2024)
Mathematics at Columbia University. Hamilton is known for contributions to geometric analysis and partial differential equations, and particularly for developing
Richard_S._Hamilton
Branch of mathematics
also known as asymptotic geometric analysis or high-dimensional geometry, is a field of mathematics that investigates the geometric properties of finite-dimensional
Asymptotic_geometry
French mathematician
French mathematician whose research concerns differential geometry and geometric analysis. He is a professor at Caltech. In 2018, he proved Yau's conjecture
Antoine_Song
Chinese mathematician (born 1958)
mathematical fields of Kähler geometry, Gromov-Witten theory, and geometric analysis. He is a professor of mathematics at Peking University and the Higgins
Tian_Gang
Field of mathematical analysis
theory. Annals of Global Analysis and Geometry The Journal of Geometric Analysis Atiyah–Singer index theorem Geometric analysis Lie groupoid Pseudogroup
Global_analysis
American mathematician
the Notices of the American Mathematical Society and The Journal of Geometric Analysis. Steven Krantz grew up in Redwood City, California and graduated from
Steven_G._Krantz
American mathematician
Technology. Her primary research interest is in geometric analysis with a particular focus on geometric analysis on singular spaces, dynamics, mathematical
Julie_Rowlett
Chinese-American mathematician (born 1949)
contributors to the development of modern differential geometry and geometric analysis. The impact of Yau's work are also seen in the mathematical and physical
Shing-Tung_Yau
Israeli mathematician and professor
the Erdős Prize. She specializes in convex geometry and asymptotic geometric analysis, and is a professor of mathematics at Tel Aviv University. Artstein
Shiri_Artstein
Sum of an (infinite) geometric progression
In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant
Geometric_series
Branch of computer science
stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered
Computational_geometry
Israeli mathematician (born 1978)
supervision of Vitali Milman. Klartag made contributions in asymptotic geometric analysis and won the 2008 EMS Prize, as well as the 2010 Erdős Prize. He is
Bo'az_Klartag
Differential geometry textbook
Curvature of Space and Time, with an Introduction to Geometric Analysis is an undergraduate-level textbook for mathematics and physics students on differential
Curvature of Space and Time, with an Introduction to Geometric Analysis
Curvature_of_Space_and_Time,_with_an_Introduction_to_Geometric_Analysis
Chinese mathematician
research contributions to the Ricci flow, a topic in the field of geometric analysis. Cao received his B.A. from Tsinghua University in 1981 and his Ph
Huai-Dong_Cao
Italian-born American mathematician (1923–2023)
MR 2682326. Zbl 1246.53001. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Universitext (Seventh edition of 1995 original ed.). Cham: Springer
Eugenio_Calabi
Canadian mathematician
1959) is a Belgian and Canadian mathematician whose research concerns geometric analysis, differential geometry, and mathematical physics. He is a Distinguished
Niky_Kamran
Data analysis technique
of data analysis known as geometric data analysis. This involves the development of direct connections between simple correspondence analysis, principal
Multiple correspondence analysis
Multiple_correspondence_analysis
American mathematician
Berkeley. Her research interests include geometric analysis and the intersection of algebra and geometric measure theory. Harrison grew up in Tuscaloosa
Jenny_Harrison
Canadian mathematician
the University of British Columbia. She is known for her work in geometric analysis and the theory of minimal surfaces. Her research is particularly focused
Ailana_Fraser
2002 book
mixture of arithmetic and geometric design principles. The book represents the state of the art for its time in the geometric analysis of medieval architecture
Ad Quadratum: The Practical Application of Geometry in Medieval Architecture
Ad_Quadratum:_The_Practical_Application_of_Geometry_in_Medieval_Architecture
Japanese mathematician (born 1948)
geometry, dynamical systems, probability, graph theory, discrete geometric analysis, and mathematical crystallography. Among his numerous contributions
Toshikazu_Sunada
Calculus of vector-valued functions
in mathematics, particularly in differential geometry, geometric topology, and harmonic analysis, in particular yielding Hodge theory on oriented pseudo-Riemannian
Vector_calculus
N-th root of the product of n numbers
In mathematics, the geometric mean (also known as the mean proportional) is a mean or average which indicates a central tendency of a finite collection
Geometric_mean
Australian mathematician
professor at the Massachusetts Institute of Technology who works on geometric analysis, partial differential equations, and differential geometry. Melrose
Richard_Burt_Melrose
volume-preserving affine transformations. Ahlfors theory A part of complex analysis being the geometric counterpart of Nevanlinna theory. It was invented by Lars Ahlfors
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Awarded every year by the American Mathematical Society
ISBN 978-1-4704-7973-2. Helgason, Sigurður (2000) [1984]. Groups and Geometric Analysis. Mathematical Surveys and Monographs. Vol. 83 (2nd ed.). Providence:
Leroy_P._Steele_Prize
Linear algebra aspects of graph theory
Mathematics. ISBN 0-444-70361-6. Sunada, Toshikazu (2008), "Discrete geometric analysis", Analysis on Graphs and Its Applications, Proceedings of Symposia in Pure
Spectral_graph_theory
British mathematician
"his foundational work on multilinear inequalities in harmonic and geometric analysis, and for a number of major results in the theory of oscillatory integrals
Jonathan Bennett (mathematician)
Jonathan_Bennett_(mathematician)
Alexandrov's soap bubble theorem is a mathematical theorem from geometric analysis that characterizes a sphere through the mean curvature. The theorem
Alexandrov's soap bubble theorem
Alexandrov's_soap_bubble_theorem
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra
Geometric_algebra
Italian mathematician
equations and calculus of variations, with several contributions to geometric analysis. Malchiodi received his Ph.D. in mathematics from the International
Andrea_Malchiodi
Sequence of operations for a task
Messages. He gave the first description of cryptanalysis by frequency analysis, the earliest codebreaking algorithm. Weight-driven clocks were a key European
Algorithm
Computer-aided design software
interactive geometry editor, ray tracing support for graphics rendering and geometric analysis, computer network distributed framebuffer support, scripting, image-processing
BRL-CAD
Australian mathematician (born 1945)
mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently
Leon_Simon
Icelandic mathematician (1927–2023)
has been devoted to the geometry and analysis on symmetric spaces. In particular, he used new integral geometric methods to establish fundamental existence
Sigurður Helgason (mathematician)
Sigurður_Helgason_(mathematician)
Danish mathematician
Tobias Holck Colding (born 1963) is a Danish mathematician working on geometric analysis, and low-dimensional topology. He is the great-grandchild of Ludwig
Tobias_Colding
starting points for the development of asymptotic geometric analysis (also called asymptotic functional analysis or the local theory of Banach spaces). For every
Dvoretzky's_theorem
Concept in mathematics
themselves, are among the most widely studied topics in the field of geometric analysis. The discovery of the "bubbling" of sequences of harmonic maps, due
Harmonic_map
British mathematician
Peter Topping (born 1971) is a British mathematician working in geometric analysis. He obtained his PhD in 1997 at the University of Warwick under the
Peter_Topping
Branch of mathematics studying functions of a complex variable
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that studies complex-valued
Complex_analysis
Russian mathematician (born 1989)
a Russian mathematician, specializing in harmonic analysis, potential theory, and geometric analysis. Logunov received his Candidate of Sciences (PhD)
Aleksandr Logunov (mathematician)
Aleksandr_Logunov_(mathematician)
Branch of mathematics
algebra means that his work must remain a piece of mid-17th century geometrical analysis of mainly historic interest. Bressoud, David M. (2011). "Historical
Calculus
Mathematics award
harmonic analysis, and combinatorial geometry." (prize was rejected by Peter Scholze) 2017 Geordie Williamson – "For pioneering work in geometric representation
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
Japanese applied mathematician and academic administrator
1960) is a Japanese applied mathematician, specializing in discrete geometric analysis and crystallography, and an academic administrator. She is the executive
Motoko_Kotani
Study of discrete mathematical structures
geometry applies algorithms to geometrical problems and representations of geometrical objects, while computer image analysis applies them to representations
Discrete_mathematics
Interactive theorem prover software
L.S. van Benthem Jutting in 1977 to formalize Landau's Foundations of Analysis, which was the first formalization of the real numbers. In 1973, Robert
Proof_assistant
the writings of Aristotle about the motion of animals related to geometric analysis. Iatromathematicians considered the bodies functioning to be measured
Iatromathematicians
Probability distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution
Geometric_distribution
Italian mathematician (born c.1981)
Sciences. Tosatti does research on complex and differential geometry; geometric analysis on complex, Hermitian, and symplectic manifolds; and partial differential
Valentino_Tosatti
Russian mathematician
mathematician, specializing in differential, Riemannian, Finsler geometry, geometric analysis, dynamical systems, and applications to mathematical physics. He is
Dmitri_Burago
Canadian-American mathematician (1925–2020)
foundational figure in the field of geometric analysis, with many of his works being closely related to the study of complex analysis and differential geometry
Louis_Nirenberg
Mathematical element in composite engineering
orientation of the fibers and the architecture of the fibers. The geometric analysis of the composite can be seen in the cross-section of the composite
Fiber_volume_ratio
Geometric analysis of multi-DoF kinematic chains that model a robot
Robotics: Mechanics and Control (3rd Edition), Prentice-Hall. J. M. McCarthy and G. S. Soh, Geometric Design of Linkages, 2nd Edition, Springer 2010.
Robot_kinematics
Ukrainian-Israeli mathematician (born 1939)
large (finite) dimension, which led to the development of asymptotic geometric analysis. His results in this field include Milman's reverse Brunn–Minkowski
Vitali_Milman
Tensor in differential geometry
fundamental in Riemannian geometry and geometric analysis. Bounds on Ricci curvature imply strong global geometric and topological consequences, as in Myers's
Ricci_curvature
Vector field on a pseudo-Riemannian manifold that preserves the metric tensor
ISBN 9789389055320. Jost, Jurgen (2002). Riemannian Geometry and Geometric Analysis. Berlin: Springer-Verlag. ISBN 3-540-42627-2. A Stehney; RS Millman
Killing_vector_field
Branch of mathematics concerning probability
discrete uniform, Bernoulli, binomial, negative binomial, Poisson and geometric distributions. Important continuous distributions include the continuous
Probability_theory
Norwegian international mathematics prize
with the award committee citing "the fundamental impact of her work on analysis, geometry and mathematical physics. The Bernt Michael Holmboe Memorial
Abel_Prize
Riemannian metric on the manifold. They are useful in many problems of geometric analysis due to their regularity properties. In two dimensions, certain harmonic
Harmonic_coordinates
American statistician
low-dimensional representations for high-dimensional data problems (multiscale geometric analysis), development of wavelets for denoising and compressed sensing. He
David_Donoho
American mathematician
working in partial differential equations, mathematical physics, geometric analysis, and integral geometry with applications to medical imaging. Peter
Peter_Kuchment
Calculus on stochastic processes
Black–Scholes–Merton model, the price of the underlying asset is modeled as a geometric Brownian motion, a particular Itô process. Besides the classical Itô and
Stochastic_calculus
Analysis of geometric properties
Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used
Statistical_shape_analysis
American mathematician
Prize in mathematical analysis. Her research connects the calculus of variations, partial differential equations, and geometric analysis, and includes the
Robin_Neumayer
Study of vector bundles, principal bundles, and fibre bundles
vector bundles, and so there are strong links between gauge theory and geometric analysis. These equations are often physically meaningful, corresponding to
Gauge_theory_(mathematics)
Area in mathematics devoted to the study of finitely generated groups
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups by exploring the connections between algebraic properties
Geometric_group_theory
These equations are of interest in geometric PDEs (a subfield at the interface between both geometric analysis and PDEs) and differential geometry.
Hessian_equation
Regularity in sensory qualia or abstract ideas
well as a connection with mathematics. A geometric pattern is a type of pattern formed of repeating geometric shapes and typically repeated like a wallpaper
Pattern
Japanese mathematician
discontinuous groups (lattice in Lie groups) and the application of geometric analysis to representation theory. He was a major developer in particular of
Toshiyuki_Kobayashi
Point minimizing sum of distances to given points
In geometry, the geometric median of a discrete point set in a Euclidean space is the point minimizing the sum of distances to the sample points. This
Geometric_median
Riemannian metrics, complex manifolds
Monge–Ampère equation, was an influential early result in the field of geometric analysis. More precisely, Calabi's conjecture asserts the resolution of the
Calabi_conjecture
Physical theory with fields invariant under the action of local "gauge" Lie groups
work of Hermann Weyl in 1918. Weyl, in an attempt to generalize the geometrical ideas of general relativity to include electromagnetism, conjectured
Gauge_theory
Theorem in complex analysis
In the mathematical fields of differential equations and geometric analysis, the maximum principle is one of the most useful and best known tools of study
Maximum_principle
Mathematician (born 1969)
Fellow of the American Mathematical Society for "contributions to geometric analysis, particularly to Ricci flow, and for mentorship". Since 2025, Ni has
Lei_Ni
Hungarian mathematician
currently a professor at Northwestern University. His research deals with geometric analysis and complex differential geometry (Kähler manifolds), including the
Gábor_Székelyhidi
Atiyah–Singer index theory and other aspects of geometric analysis involving Dirac type operators. In Clifford analysis one also considers differential operators
Clifford_analysis
American mathematician (born 1950)
American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984
Richard_Schoen
Algebra based on a vector space with a quadratic form
analysis Clifford module Complex spin structure Dirac operator Exterior algebra Fierz identity Gamma matrices Generalized Clifford algebra Geometric algebra
Clifford_algebra
Right inverse of a fiber bundle map
( U , E ) {\displaystyle C^{\infty }(U,E)} . It is also useful in geometric analysis to consider spaces of sections with intermediate regularity (e.g.
Section_(fiber_bundle)
Polyhedron with 12 faces
Reality Polyhedra The Encyclopedia of Polyhedra K.J.M. MacLean, A Geometric Analysis of the Five Platonic Solids and Other Semi-Regular Polyhedra Dodecahedron
Dodecahedron
Fundamental theorem in probability theory and statistics
(2012). Topological Crystallography – With a View Towards Discrete Geometric Analysis. Surveys and Tutorials in the Applied Mathematical Sciences. Vol. 6
Central_limit_theorem
Public park system in Barcelona, Spain
organic forms led to innovative structural solutions based on geometric analysis. These geometric insights gave rise to his imaginative and ornamental style
Park_Güell
Chinese mathematician (born 1991)
1991) is a Chinese mathematician known for her research in Fourier analysis and geometric measure theory. She was awarded the Fields Medal in 2026 for her
Hong_Wang
Chinese-American mathematician
Taylor. Geometry Analysis and Topology of Discrete Groups; by Lizhen Ji, Kefeng Liu, and Yang Lo. Handbook of Geometric Analysis; by Lizhen Ji. Mathematics
Lizhen_Ji
Application of mathematical methods to other fields
mathematics. Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed
Applied_mathematics
Software used in mathematical applications
is software used to model, analyze or calculate numeric, symbolic or geometric data. Mathematical knowledge of techniques such as algorisms which existed
Mathematical_software
Branch of applied probability theory
prescriptive approach (how people ought to make decisions) is called decision analysis and is aimed at finding tools, methodologies, and software (decision support
Decision_theory
Form of an object
it is approximately the same geometric object as an actual geometric disk. A geometric shape consists of the geometric information which remains when
Shape
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GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
GEOMETRIC ANALYSIS
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